622
An ordered pair of sets G = (V, E) where V is a
nonempty finite set and E consisting of 2‐element
subsets of elements of V is called a graph. It is
denotedbyG=(V,E).Viscalledvertexandedgeset
respectively. The elements in
V and E are called
vertices and edges respectively. If elements of E are
ordered pairs, then G is called a directed graph or
digraph. The vertices between which an edge exists
are called endpoints of the edge. An edge whose
endpoints are the same is called a loop. A
graph
withoutloopsiscalledasimplegraph.
Foragivensourcevertex(node)inthegraph,the
algorithm finds the path with lowest cost (ie the
shortest path) between that vertex and every other
vertex.Itcanalsobeusedforfindingtheshortestcost
path from one vertex to
a destination vertex by
stoppingthealgorithmisdeterminedbytheshortest
path to the destination node. For example, if the
vertices of the graph represent the city and are the
costs of running paths edge distances between pairs
of cities connected directly to the road, Dijkstraʹs
algorithm can
be used to find the shortest route
betweenonecityandallothercities.Asaresult,the
shortest path algorithm is widely used routing
protocols in a network, in particular the IS‐IS and
OpenShortestPathFirst.(Neumann,2014)
Short characteristic of Dijsktra algorithm
(Neumann,2016a).
Theinputofthealgorithmconsistsofaweighted
directedgraphGandasourcevertexsinG
DenoteVasthesetofallverticesinthegraphG.
Each edge of the graph is an ordered pair of
vertices(u,v)
This representing a connection from vertex u to
vertexv
ThesetofalledgesisdenotedE
Weights of edges are given by a weight function
w:E → [0,∞)
Therefore w(u,v) is the cost of moving directly
fromvertexutovertexv
The cost of an edge can be thought of as (a
generalizationof)thedistancebetweenthosetwo
vertices
Thecostofapathbetweentwoverticesisthesum
ofcostsoftheedgesinthatpath
For a given pair of vertices s and t in V, the
algorithm finds the path from s to t with lowest
cost(i.e.theshortestpath)
It can also be used for finding costs of shortest
pathsfromasinglevertexstoallotherverticesin
thegraph.
Figure4.Dijkstrasalgorithmontreegraph
The Dempster‐Shafer and Dijkstra algorithms are
well known. The Dijjksta algorithm was first
published almost a half a century ago. To this day,
findingconnectionsbetweenverticesisused.Butnot
alwaystheshortestpathisthebest. Itisto consider
various
criteria. This paper is an introduction to
furtherresearch.
In this study was developed a model of the ship
routing network that solves problems optimal path
using a modified version of Dijkstraʹs shortest path
algorithm and the ba sic function of the reaction
vessel.Wasestablishedfidelitymodelsbytesting.
As
you can see, the model avoids the adverse weather
conditions and solves the path of least time to your
destination.Itcalculatestheusefultime,distance,fuel
consumption and metrics to quantify routing
decisions. All calculations was made by intervals.
(Neumann,2015)
7 CONCLUSIONS
The proliferation of modern electronics systems
is
already exaction the duration for user input and
superintendencesystems.Telematics willberequisite
tostaythe development multitudeofuser‐selectable
input attendant and points within the vehicle. As
carriage come more complicated they will
increasingly confide on telematics and driver notice
systemsthatwillcometheuser
interfacetobothon‐
board and off board enlightenment. Government
commission and homogenous actions are already
composednecessarilyfortelematicssystems.Hands‐
freemobilephonecommissionaregrowthfastdueto
driverfuriousnessegress.Itisprobablethatlow‐end
telematics with a harangue user interface and radio
system integration will
come the elect solutions. ITS
willenlarge in adulteration over the next decennary
andwillincreasinglyneedtelematicscapabilities.As
huge as the self‐propelled telematics hardware and
benefit opportunities may be, the circuitous benefits
effectual from the worth of telematics data may be
alike essential. The circuitous telematics benefits
softenthelocomotiveassurancediligence,healthcare
providers,generalsafenessagencies andmanyother
industries. The price savings, price annulment and
amended functional efficiencies external the
telematics assiduity will be graduated in 15 to 20
years.(Juliussen,2003)
REFERENCES
Bekiaris, E., Nakanishi, Y., 2004. Economic impact of
intelligent transportation systems: innovation and case
study.
Boominathan, P., Kanchan, A., 2014. Routing Planning As
AnApplicationOf GraphTheory.International journal
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Chang, S.‐H., Fan, C.‐Y., 2016. Identification of the
technology life cycle of
telematics: A patent‐based
analytical perspective. Technological Forecasting and
Social Change 105, 1–10.
https://doi.org/10.1016/j.techfore.2016.01.023
Chen, A., Jain, N., Perinola, A., Pietraszek, T., Rooney, S.,
Scotton, P., 2004. Scaling real‐time telematics
applications using programmable middleboxes: a case
study in traffic prediction, in: First IEEE Consumer
Communications and Networking Conference, 2004.
CCNC 2004. Presented at the First IEEE Consumer
Communications and Networking Conference, 2004.